I am running 2 monitors, and my left (secondary) monitor sometimes exhibits odd behavior with regards to the mouse. For example, if I have an IE window on the second monitory, and I place the cursor over the title bar, the cursor will change to whatever shape it entered the window as, i.e. if I come in from the top (over the top resizing border) it's an up-down resizing button. If I come in from the corner, it stays as a diagonal resizing button.

It gets very annoying when you rely on the cursor for visual clues, like when the computer is busy. It changes to an hourglass, but it never changes back, until I move over something else that will force the cursor to change.

I'd have to guess that the second monitor isn't firing mouse-leaving or possibly mouse-over events, but what would cause that?

Any time that I have seen that kind of behaviour I find it is typically related to the program in which the mouse cursor goes awry, and it is always temporary. I've had this happen in Visual Studio, Firefox, and IE. I have also had this happen on single monitor setups, as well as dual, so (at least in my case) it's not related to the dual monitor setup.

As @Wil mentioned though, if I would suspect anything about the dual monitor setup, I would look at the multi-monitor tools for the graphics driver. Sometimes they like to add little tool buttons in the title bar for things like "Move this window to the other monitor" and such.